Question:medium

The perimeter of a rectangle is 60 cm. If its length is twice its breadth, then its area is:

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With sides in a fixed ratio, convert perimeter into a single variable first; then compute the area.
Updated On: Jul 15, 2026
  • 200 cm$^2$
  • 180 cm$^2$
  • 160 cm$^2$
  • 220 cm$^2$
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The Correct Option is A

Approach Solution - 1

Step 1: Express the sides as ratio parts.
Since the length is twice the breadth, write breadth as 1 part and length as 2 parts, so length plus breadth together make 3 parts.

Step 2: Link the parts to the perimeter.
Perimeter \( = 2(\text{length} + \text{breadth}) = 2 \times 3 \text{ parts} = 6 \text{ parts} \). Given the perimeter is 60 cm, each part is worth \( 60 \div 6 = 10 \) cm.

Step 3: Find the actual sides.
Breadth \( = 1 \text{ part} = 10 \) cm, and length \( = 2 \text{ parts} = 20 \) cm.

Step 4: Compute the area.
Area \( = \text{length} \times \text{breadth} = 20 \times 10 = 200 \, \text{cm}^2 \).
\[ \boxed{200 \, \text{cm}^2} \]
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Approach Solution -2

Since length is always twice the breadth in this problem, it is possible to derive a single formula linking area directly to the perimeter, then just substitute the given perimeter once instead of solving for the sides first.

  1. 200 cm2: Writing breadth as \( b \), perimeter \( = 2(2b + b) = 6b \), so \( b = \frac{\text{Perimeter}}{6} \). Area \( = 2b^2 = 2\left(\frac{\text{Perimeter}}{6}\right)^2 \). Substituting Perimeter \( = 60 \), Area \( = 2 \times \left(\frac{60}{6}\right)^2 = 2 \times 10^2 = 200 \) sq cm, matching this option.
  2. 180 cm2: The derived formula gives a single, fixed area of 200 sq cm for a perimeter of 60 cm, so 180 cannot be the result of this same formula.
  3. 160 cm2: Likewise, this value does not equal \( 2 \times 10^2 \), so it falls outside what the formula produces for this perimeter.
  4. 220 cm2: This too does not match the fixed value the formula gives, so it does not fit either.

The derived formula \( \text{Area} = 2\left(\frac{\text{Perimeter}}{6}\right)^2 \) leaves only one possible value once the perimeter of 60 cm is substituted.

So the correct answer is 200 cm2.

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